Relations in the tautological ring of the moduli space of curves

Abstract

The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in successively simpler forms. The final result is the proof of the Faber-Zagier relations (conjectured in 2000).

56 pages. Final version to appear in PAMQ (Mumford volume). arXiv admin note: text overlap with arXiv:1101.2236

References in corpus (6)

• Relations in the tautological ring
• Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$
• Pixton's double ramification cycle relations
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Relations in the tautological ring of $M_g$
• On the tautological rings of M_{g, 1} and its universal Jacobian

Cited by in corpus (16)

• Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• Relations on Mbar_{g,n} via 3-spin structures
• Tautological relations in moduli spaces of weighted pointed curves
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Relations among characteristic classes of manifold bundles
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
• Special codimension one loci in Hurwitz spaces
• The Chern classes of the Verlinde bundles
• Canonical metric on the space of symplectic invariant tensors and its applications
• Tautological classes with twisted coefficients
• Cycles on curves and Jacobians: a tale of two tautological rings
• Socle pairings on tautological rings
• Relations on Mbar_{g,n} via orbifold stable maps
• Complete descriptions of the tautological rings of the moduli spaces of curves of genus lower or equal to 4 with marked points
• Relations in the Tautological Ring of the Universal Curve